In the US, back when I did a lot of renovation work, they were called "finished attic", or "converted attic". A "loft" here generally refers to converted commercial space into living units. If someone told me they designed "lofts" I would assume converted commercial space.
Funny thing though, which makes it all somewhat meaningless, is a one story house with a finished room under the roof, and built that way, is simply a one and a half story. The same one story house that later has the attic finished, is a house with a finished attic:)
Best use a few adjectives.... |ˈajiktiv| noun Grammar... a word or phrase naming an attribute, added to or grammatically related to a noun to modify or describe it.